Mathematics Questions and Answers – Conditional Probability

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This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Conditional Probability”.

1. If E and F are two events associated with the same sample space of a random experiment then P (E|F) is given by _________
a) P(E∩F) / P(F), provided P(F) ≠ 0
b) P(E∩F) / P(F), provided P(F) = 0
c) P(E∩F) / P(F)
d) P(E∩F) / P(E)
View Answer

Answer: a
Explanation: E and F are two events associated with the same sample space of a random experiment.
The value of P (E|F) = (E∩F) / P(F), provided P(F) ≠ 0. We know that if P(F) = 0, then the value of P(E|F) will reach a value which is not defined hence it is wrong option. Also, P(E∩F) / P(F) and P(E∩F) / P(E) are wrong and do not equate to P(E|F).
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2. Let E and F be events of a sample space S of an experiment, if P(S|F) = P(F|F) then value of P(S|F)
is __________
a) 0
b) -1
c) 1
d) 2
View Answer

Answer: c
Explanation: We know that P(S|F) = P(S∩F) / P(F). (By formula for conditional probability)
Which is equivalent to P(F) / P(F) = 1, hence the value of P(S|F) = 1.

3. Given that E and F are events such that P(E) = 0.6, P(F) = 0.3 and P(E∩F) = 0.2, then P(E|F) ?
a) 2/3
b) 1/3
c) 3/4
d) 1/4
View Answer

Answer: a
Explanation: We know that P(E|F) = P(E∩F) / P(F). (By formula for conditional probability)
Value of P(E∩F) is given to be 0.2 and value of P(F) is given to be 0.3.
P(E|F) = (0.2) / (0.3).
P(E|F) = 2 / 3.
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4. Given that E and F are events such that P(E) = 0.5, P(F) = 0.4 and P(E∩F) = 0.3, then what will be the value of P(F|E)?
a) 2/5
b) 3/5
c) 3/4
d) 2/4
View Answer

Answer: b
Explanation: We know that P(F|E) = P(E∩F) / P(E). (By formula for conditional probability)
Value of P(E∩F) is given to be 0.3 and value of P(E) is given to be 0.5.
P(F|E) = (0.3) / (0.5).
P(F|E) = 3 / 5.

5. Let E and F be events of a sample space S of an experiment, if P(S|F) = P(F|F), then value of P(F|F)
is __________
a) 0
b) -1
c) 1
d) 2
View Answer

Answer: c
Explanation: We know that P(S|F) = P(S∩F) / P(F). (By formula for conditional probability)
Which is equivalent to P(F|F) = P(F) / P(F) = 1, hence the value of P(F|F) = 1.
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6. If P(A) = 7/11, P(B) = 6 / 11 and P(A∪B) = 8/11, then P(A|B) = ________
a) 3/5
b) 2/3
c) 1/2
d) 1
View Answer

Answer: d
Explanation: We know that P(A|B) = P(A∩B) / P(B). (By formula for conditional probability)
Also P(A∪B) = P(A)+P(B) – P(A∩B). (By formula of probability)
\(\Rightarrow\) 8/11 = 7/11 + 6/11 – P(A∩B)
\(\Rightarrow\) P(A∩B) = 13/11 – 7/11
\(\Rightarrow\) P(A∩B) = 6/11
P(A|B) = (6/11) / (6/11).
P(A|B) = 1.

7. If P(A) = 1/5, P(B) = 0, then what will be the value of P(A|B)?
a) 0
b) 1
c) Not defined
d) 1/5
View Answer

Answer: c
Explanation: We know that P(A|B) = P(A∩B) / P(B). (By formula for conditional probability)
The value of P(B) = 0 in the given question. As the value of denominator becomes 0, the value of P(A|B) becomes un-defined.
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8. If P(A) = 5/13, P(B) = 7/13 and P(A∩B) = 3/13, evaluate P(A|B).
a) 1/7
b) 3/7
c) 3/5
d) 2/7
View Answer

Answer: b
Explanation: We know that P(A|B) = P(A∩B) / P(B). (By formula for conditional probability)
Which is equivalent to (3/13) / (7/13), hence the value of P(A|B) = 3/7.

Sanfoundry Global Education & Learning Series – Mathematics – Class 12.

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Manish Bhojasia - Founder & CTO at Sanfoundry
Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn | Youtube | Instagram | Facebook | Twitter